course Phys 202 I just took the MCAT this past weekend and studying for it kind of took over my life. I know I'm behind, but I will catch up by the August 10th deadline. I just wanted to let you know why my work stopped for awhile. 010. `query 9 *********************************************
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Given Solution: ** we know how many wavelength segments will pass every second, and we know the length of each, so that multiplying the two gives us the velocity with which they must be passing ** Your Self-Critique: OK Your Self-Critique rating: OK ********************************************* Question: explain how we can reason out that the period of a periodic wave is equal to its wavelength divided by its velocity YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your Solution: We know from the precious example that f = v/lamda Period is just 1/f so it is lamda (wavelength)/v or m/m/sec = sec^ -1 = period Confidence rating: 3
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Given Solution: ** If we know how far it is between peaks (wavelength) and how fast the wavetrain is passing (velocity) we can divide the distance between peaks by the velocity to see how much time passes between peaks at a given point. That is, period is wavelength / velocity. ** Your Self-Critique: OK Your Self-Critique rating: OK ********************************************* Question: explain why the equation of motion at a position x along a sinusoidal wave is A sin( `omega t - x / v) if the equation of motion at the x = 0 position is A sin(`omega t) YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your Solution: You have to include a factor to take into account the lag time in which it takes to get from x position 0 to the new position. This accounts for the – x/v in the parenthesis. This is the time lab because you are subtracting the position x divided by its velocity which gives you the excess time. m divided by m/s = seconds Confidence rating: 3
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Given Solution: ** the key is the time delay. Time for the disturbance to get from x = 0 to position x is x / v. What happens at the new position is delayed by time x/v, so what happens there at clock time t happened at x=0 when clock time was t = x/v. In more detail: If x is the distance down the wave then x / v is the time it takes the wave to travel that distance. What happens at time t at position x is what happened at time t - x/v at position x=0. That expression should be y = sin(`omega * (t - x / v)). The sine function goes from -1 to 0 to 1 to 0 to -1 to 0 to 1 to 0 ..., one cycle after another. In harmonic waves the motion of a point on the wave (think of the motion of a black mark on a white rope with vertical pulses traveling down the rope) will go thru this sort of motion (down, middle, up, middle, down, etc.) as repeated pulses pass. If I'm creating the pulses at my end, and that black mark is some distance x down in rope, then what you see at the black mark is what I did at time x/v earlier. ** STUDENT COMMENT (University Physics): According to the Y&F book (p.553) we get the expression for a sinusoidal wave moving the the +x-direction with the equation: Y(x,t) = A*cos[omega*(t-x/v)] I am not sure where the sine came from in the equation in the question. The book uses the cosine function to represent the waves motion.